A Survey of Statistical Network Models

By Anna Goldenberg, Alice X. Zheng, Stephen E. Fienberg, Edoardo M. Airoldi. Found. Trends Mach. Learn., 2009

1,002 citations recorded by the source corpus.

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

Subfields: Experimental and Cognitive Psychology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76aeda698f79c97636184237d38cbd1e53ce077e

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Citations in the corpus

Consistency of spectral clustering in stochastic block models (2013, methodology): “A review of modeling and inference on network data can be found in Kolaczyk (2009), Newman (2009), and Goldenberg et al. (2010).”
FAST COMMUNITY DETECTION BY SCORE (2012, methodology): “The comparison of DCBM with the p ∗ model and the ERGM [14, 23] is not obvious, given that all of them use a large number of parameters.”
Probabilistic Latent Document Network Embedding (2014, methodology): “Finally, we compare the effectiveness of PLANE as a topic model for document network (V-D).”
Point Patterns Occurring on Complex Structures in Space and Space-Time: An Alternative Network Approach (2016, background): “Another family of structural models for planar point processes that is similar in spirit, but different in detail, was presented by Okabe and Yamada (2001) as well as Ang (2010) and Ang et al.”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, background): “Statistical inference on random graphs and networks, in particular, has witnessed extraordinary growth over the last decade: for example, [41, 51] discuss the considerable applications in recent network science of several canonical random graph models.”
Discovering Latent Network Structure in Point Process Data (2014, methodology): “A rich literature has arisen in recent years for applying statistical machine learning models to this type of problem, e.g., Liben-Nowell & Kleinberg (2007); Hoff (2008); Goldenberg et al. (2010).”
A Survey of Link Prediction in Complex Networks (2016, methodology): “Many network formation models have been successfully described in terms of statistical and probabilistic concepts [Goldenberg et al. 2010].”
Similarity network fusion for aggregating data types on a genomic scale (2014, neutral): “8 – 10 ).”
A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs (2011, methodology): “These statistical models use random graphs to model relationships between objects; Goldenberg (2009) provided a review of statistical models for networks.”
Efficient discovery of overlapping communities in massive networks (2013, background): “In particular, we posit a probabilistic model of networks (23) where each node can belong to multiple communities (10).”
Relational Deep Learning: A Deep Latent Variable Model for Link Prediction (2017, methodology): “Roughly speaking, existing link prediction methods can be categorized into three classes (Goldenberg et al. 2010): link-based methods, attribute-based methods, and hybrid methods.”
Handbook of Big Data (2016, background): “For more extensive surveys of the literature on random graph models, see Goldenberg et al. (2010) and Kolaczyk (2009).”
Consistency of community detection in networks under degree-corrected stochastic block models (2011, methodology): “Networks have become one of the more common forms of data, and network analysis has received a lot of attention in computer science, physics, social sciences, biology and statistics (see [13, 15, 25] for reviews).”